解由冪函數(shù)f(x)=X^(m2-2m-3)在區(qū)間(0,+∞)上是減函數(shù)
則m^2-2m-3＜0
即（m-3）（m+1）＜0
即-1＜m＜3
又由m∈z
故m=0,1,2,
當(dāng)m=0時(shí),函數(shù)為f（x）=x^(-3)是奇函數(shù)
當(dāng)m=1時(shí),函數(shù)為f（x）=x^(-4)是偶函數(shù)
當(dāng)m=2時(shí),函數(shù)為f（x）=x^(-3)是奇函數(shù)
故m=0或2.